Yes, Systematic Risk cannot be avoided by the inclusion of more stocks, since it is inherent in the overall market.

However, Systematic risk can be magnified through selection or by using leverage, or diminished by including securities that have a low correlation with the portfolio, assuming they are not already part of the portfolio.

Therefore, while it cannot be eliminated, there is no reason that it must remain constant as the number of stocks in a portfolio increase.

Moreover, the only risk relevant in determining expected returns is Systematic Risk (as represented by the beta in CAPM). Why? Becasue in theory, rational investors are expected to completely diversify away the idiosyncratic risk/diversifiable risk.

Maybe what I do not get is why beta represents systematic risk. If the market has its own risk (beta = 1), and a company has a beta of 1.5, how do you explain the 1.5 number in the context of a portfolio?

The beta represents an asset’s sensitivity to market risk (aka systematic risk, non-diversifiable risk)

So if the the “market portfolio” were to increase (decrease) in value by 1%, an asset with beta 1.5 suggests that the asset value would increase (decrease) by 1.5%.

The same 1% increase in the market portfolio, will have different impacts on the other assets in the portfolio as determined by their corresponding betas.

To understand the portfolio effect you would calculate the portfolio beta - the individual asset betas are used to compute a weighted mean with weights being the proportion of each asset in the total portfolio value.

The sections in portfolio management will cover these concepts with plenty of examples.

So, basically, beta for a portfolio cannot become zero (eliminated) but you can change it from 1.5 to 2 or back down to 1 with the inclusion of certain securities in the portfolio?

A beta from a protfolio could theoretically become zero. The portfolio beta is simply a (market) weighted average of the individual stocks’ betas. To get to a negative beta,

Include negative beta securityto offset the positive beta securities in the portfolio (note: this is difficult to do other than by using derivatives)

Take short positions in positive beta securities. Since a short position is effectively a negative weight, the contribution to portfolio beta of a short position is the same as a long position in a negative beta security.